Characterizing the Optimility of Minimal SSA Using the Value Flow Graph

In this paper, we introduce a graph representation called the Value Flow Graph (VFG). The VFG represents the ow of values between the versions of the same variable in the Static Sigle Assignment (SSA) form and visually characterizes the properties of SSA. We show the conventional deenition of the (most commonly used) SSA form is overly conservative and propose a new relaxed variation of SSA form. We then discuss and characterize the optimality, in terms of size, of the proposed form and of the conventional SSA form with the minimality of the VFG.